1. Out of the following operators (|, *, +, &, $), the one having lowest priority is ________
a) +
b) $
c) |
d) &
Explanation: According to the algorithm (infix-prefix), it follows that the logical OR will have the lowest priority.
2. What would be the Prefix notation for the given equation?
A^B^C^D
a) ^^^ABCD
b) ^A^B^CD
c) ABCD^^^
d) AB^C^D
Explanation: Reverse the equation or scan the equation from right to left. Apply the infix-prefix algorithm. Here we have to remember that the exponentiation has order of associativity from right to left. Therefore the stack goes on pushing ^. Therefore resulting in ^^^ABCD.
3. What would be the Prefix notation for the given equation?
a+b-c/d & e|f
a) |&-+ab/cdef
b) &|-+ab/cdef
c) |&-ab+/cdef
d) |&-+/abcdef
Explanation: Reverse the equation or scan the equation from right to left. Apply the infix-prefix algorithm. The preference order in ascending order are as follows |&+*/.
4. What would be the Prefix notation for the given equation?
(a+(b/c)*(d^e)-f)
a) -+a*/^bcdef
b) -+a*/bc^def
c) -+a*b/c^def
d) -a+*/bc^def
Explanation: Reverse the equation or scan the equation from right to left. Apply the infix-prefix algorithm. The preference order in ascending order are as follows +*/^. Brackets have the highest priority. The equations inside the brackets are solved first.
5. What would be the Prefix notation and Postfix notation for the given equation?
A+B+C
a) ++ABC and AB+C+
b) AB+C+ and ++ABC
c) ABC++ and AB+C+
d) ABC+ and ABC+
Explanation: For prefix notation there is a need of reversing the giving equation and solving it as a normal infix-postfix question. We see that it doesn’t result as same as normal infix-postfix conversion.
6. What would be the Prefix notation for the given equation?
a|b & c
a) a|& bc
b) &|abc
c) |a & bc
d) ab&|c
Explanation: The order of preference of operators is as follows (descending): & |. The equation a|b & c will be parenthesized as (a|(b & c)) for evaluation. Therefore the equation for prefix notation evaluates to |a & bc.
7. When an operand is read, which of the following is done?
a) It is placed on to the output
b) It is placed in operator stack
c) It is ignored
d) Operator stack is emptied
Explanation: While converting an infix expression to a postfix expression, when an operand is read, it is placed on to the output. When an operator is read, it is placed in the operator stack.
8. What should be done when a left parenthesis ‘(‘ is encountered?
a) It is ignored
b) It is placed in the output
c) It is placed in the operator stack
d) The contents of the operator stack is emptied
Explanation: When a left parenthesis is encountered, it is placed on to the operator stack. When the corresponding right parenthesis is encountered, the stack is popped until the left parenthesis and remove both the parenthesis.
9. Which of the following is an infix expression?
a) (a+b)*(c+d)
b) ab+c*
c) +ab
d) abc+*
Explanation: (a+b)*(c+d) is an infix expression. +ab is a prefix expression and ab+c* is a postfix expression.
10. What is the time complexity of an infix to postfix conversion algorithm?
a) O(N log N)
b) O(N)
c) O(N2)
d) O(M log N)
Explanation: The time complexity of an infix to postfix expression conversion algorithm is mathematically found to be O(N).